The Fellowship of the Ring, also known as the Company of the Ring, was formed from nine members of the Free peoples during the War of the Ring. Its purpose was to take the One Ring to Mordor, the only place where it could be destroyed.

Although the purpose was fixed by the Council of Elrond, it was not decreed how, in what manner and through which route this could be done; such details were left to the Fellowship's discretion. As a consequence, the Fellowship started with no stable plan. One option was to go directly to Mount Doom, the other was to ask help from Boromir's father, Denethor II.

The way of how to reach the East was a problem. After moving south from Rivendell, they encountered crebain on their arrival in Hollin. Fearing that they were used as spies by Saruman, the Fellowship spent the entire day in hiding, without a campfire.

Attempting to pass Caradhras

When they had to pass the Misty Mountains; Boromir proposed the Gap of Rohan (the way through which he arrived to Rivendell), Gandalf insisted to pass through Moria but Aragorn though the Redhorn Pass would be safer. However after attempting in vain to pass the blizzard, they followed Gandalf's opinion.

Aragorn was appointed the head of the Company, and their next stop was to meet with Galadriel and Celeborn, the elf-lords of Lothlórien. They stayed there for several days, resting and counseling for their plan and route. On their leave, the elves gave them several useful gifts and gave them boats to sail the Anduin.

Frodo began to realize not only that someone was following them, but also that the Ring was having a malevolent effect on some members of the party, especially Boromir. It was he who tried to take the ring from him, after the passage through the Argonath. In the process, Frodo put on the ring to escape him, but he was followed by Sam. The rest of the Company was attacked by orcs while trying to find the Ring-bearer. Seeing no other halfling, the Orcs succeeded in capturing Merry and Pippin, killing Boromir who tried to protect them.

Boromir's last stand protecting Merry and Pippin

And so, the Fellowship was broken, but not yet disbanded. Sam followed Frodo down the Emyn Muil having decided to go to Mordor himself. Aragorn with Gimli and Legolas (the "Three Hunters") decided to follow the Orcs into Rohan and rescue Pippin and Merry. Unknown to them all, Gandalf had resurrected and visited Lothlórien after them.

Terminology

Though usually called Fellowship of the Ring in adaptations and by fans, the actual term is not used in full until the chapter Many Partings, when Elessar disbands it. In the story itself, they are usually referred to as the Fellowship, the Company of the Ring (more so than Fellowship), and the Nine Walkers (in opposition of the Nine Riders who pursued them).